Question

what is the length of the unknown leg to the nearest tenth? a 16 10 2.4 5.1 12.5 18.9

Explanation:

1. First, identify the relevant formula:

• For a right - triangle, we use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs of the right - triangle. In this case, \(c = 16\), \(b = 10\), and we want to find \(a\).
• Rearranging the Pythagorean theorem to solve for \(a\), we get \(a=\sqrt{c^{2}-b^{2}}\).

1. Then, substitute the values:

• Substitute \(c = 16\) and \(b = 10\) into the formula: \(a=\sqrt{16^{2}-10^{2}}=\sqrt{256 - 100}=\sqrt{156}\).

1. Finally, calculate and round:

• \(\sqrt{156}\approx12.5\).

Answer:

C. 12.5